Is it permissible to inform the younger sister that she owns a part of the house, knowing that the older sister, who is entrusted with the matter, does not want to inform her sister of that?

One must repent to Allah Almighty for looking at the papers without the owner's permission. It would have been better to decline accepting them from the start. There is no need to inform the younger sister about the matter unless silence would lead to the loss of her right. Ownership of the house is not established merely by the father writing it over to them. Rather, it requires the acceptance of the gift during his lifetime and its lawful قبض (taking possession) by him vacating it for them, allowing them to dispose of it as owners. Otherwise, the house remains the property of their father, and after his death, the remaining heirs will share in it.